Question

Hot combustion gases, modeled as air behaving as an ideal gas, enter a turbine at 10 bar, 1500 K and exit at 1.97 bar and 900 K. If the power output of the turbine is 55.4 kW, determine the rate of heat transfer from the turbine to its surroundings, in kW.

Answer 1

Answer:

The heat transfer from the turbine to the surrounding  Q = - 547.6 KW

Explanation:

Given data

Pressure at inlet $P_{1}$ = 10 bar

Temperature at inlet $T_{1}$ = 1500 K

Pressure at exit $P_{2}$ = 1.97 bar

Temperature at outlet $T_{2}$ = 900 K

Power output from the turbine $W_{T}$ = 55.4 KW

Apply steady flow energy equation for the turbine

$h_{1} + Q = h_{2} + W_{T}$

$Q = h_{2} - h_{1} + W_{T}$

$Q = C_{p } ( T_{2} - T_{1} ) + W_{T}$ -------- (1)

Put all the values in equation 1 we get,

Q =  1.005 ( 900 - 1500 ) + 55.4

Q = - 547.6 KW

This is the heat transfer from the turbine to the surrounding. here negative sign shows that heat is lost from the turbine to the surrounding.

Answer 2

The rate of heat transfer from the turbine is 15.4 kilowatts.

How to calculate the rate of heat transfer from the turbine

The rate of heat transfer ($\dot Q$), in kilowatts, can be found by first law of thermodynamics and equation of state for ideal states:

$-\dot Q + \dot m \cdot c_{p}\cdot (T_{1}-T_{2})-\dot W = 0$     (1)

Where:

• $\dot m$ - Mass flow, in kilograms per second.
• $T_{1}$ - Inlet temperature, in degrees Celsius.
• $T_{2}$ - Outlet temperature, in degrees Celsius.
• $c_{p}$ - Specific heat at constant pressure, in kilojoules per kilogram-degree Celsius.
• $\dot W$ - Power, in kilowatts.

If we know that $\dot m = 0.1\,\frac{kg}{s}$, $c_{p} = 1.18\,\frac{kJ}{kg\cdot ^{\circ}C}$, $T_{1} = 1500\,K$, $T_{2} = 900\,K$ and $\dot W = 55.4\,kW$, then the rate of heat transfer is:

$\dot Q = \dot m\cdot c_{p}\cdot (T_{1}-T_{2})-\dot W$

$\dot Q = \left(0.1\,\frac{kg}{s} \right)\cdot \left(1.18\,\frac{kJ}{kg\cdot ^{\circ}C} \right) \cdot (1500\,K-900\,K)-55.4\,kW$

$\dot Q = 15.4\,kW$

The rate of heat transfer from the turbine is 15.4 kilowatts. $\blacksquare$

Remark

The statement is incomplete. Correct form is shown below:

"Hot combustion gases, modeled as air behaving as an ideal gas, enter a turbine at 10 bar, 1500 K and exit at 1.97 bar and 900 K with a mass flow rate at 0.1 kilograms per second. If the power output of the turbine is 55.4 kW, determine the rate of heat transfer from the turbine to its surroundings, in kW."

To learn more on turbines, we kindly invite to check this verified question: https://brainly.com/question/928271